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WorksheetsDM UNIT 1 & 5
Total questions: 30
Worksheet time: 40mins
“The product of two negative real numbers is not negative.” Is given by?
∃x ∀y ((x < 0) ∧ (y < 0) → (xy > 0))
∃x ∃y ((x < 0) ∧ (y < 0) ∧ (xy > 0))
∀x ∃y ((x < 0) ∧ (y < 0) ∧ (xy > 0))
∀x ∀y ((x < 0) ∧ (y < 0) → (xy > 0))
Translate ∀x∃y(x < y) in English, considering domain as a real number for both the variable.
For all real number x there exists a real number y such that x is less than y
For every real number y there exists a real number x such that x is less than y
For some real number x there exists a real number y such that x is less than y
For each and every real number x and y such that x is less than y
Let P: This is a great website, Q: You should not come back here. Then ‘This is a great website and you should come back here.’ is best represented by?
~P V ~Q
P ∧ ~Q
P V Q
P ∧ Q
How many bits string of length 4 are possible such that they contain 2 ones and 2 zeroes?
4
2
5
6
Consider the following statements.
A: Raju should exercise.
B: Raju is not a decent table tennis player.
C: Raju wants to play good table tennis.
The symbolic form of “Raju is not a decent table tennis player and if he wants to play good table tennis then he should exercise.” is?
A->B->C
B∧(C->A)
C->B∧A
B<->A∧C
What is the dual of (A ∧ B) v (C ∧ D)?
(A V B) v (C v D)
(A V B) ^ (C v D)
(A V B) v (C ∧ D)
(A ∧ B) v (C v D)
A compound proposition that is neither a tautology nor a contradiction is called a ___________
Contingency
Equivalence
Condition
Inference
What is the contrapositive of the conditional statement? “The home team misses whenever it is drizzling?”
If it is drizzling, then home team misses
If the home team misses, then it is drizzling
If it is not drizzling, then the home team does not misses
If the home team wins, then it is not drizzling
Which of the following statement is correct?
p ∨ q ≡ q ∨ p
¬(p ∧ q) ≡ ¬p ∨ ¬q
(p ∨ q) ∨ r ≡ p ∨ (q ∨ r)
All of mentioned
The statement, “At least one of your friends is perfect”. Let P (x) be “x is perfect” and let F (x) be “x is your friend” and let the domain be all people.
∀x (F (x) → P (x))
∀x (F (x) ∧ P (x))
∃x (F (x) ∧ P (x))
∃x (F (x) → P (x))
A Poset in which every pair of elements has both a least upper bound and a greatest lower bound is termed as _______
sublattice
lattice
trail
walk
In the poset (Z+, |) (where Z+ is the set of all positive integers and | is the divides relation) are the integers 9 and 351 comparable?
comparable
not comparable
comparable but not determined
determined but not comparable
If every two elements of a poset are comparable then the poset is called ________
sub ordered poset
totally ordered poset
sub lattice
semigroup
______ and _______ are the two binary operations defined for lattices.
Join, meet
Addition, subtraction
Union, intersection
Multiplication, modulo division
A ________ has a greatest element and a least element which satisfy 0<=a<=1 for every a in the lattice(say, L).
semilattice
join semilattice
meet semilattice
bounded lattice
Boolean algebra can be used ____________
For designing of the digital computers
In building logic symbols
Circuit theory
Building algebraic functions
What is the use of Boolean identities?
Minimizing the Boolean expression
Maximizing the Boolean expression
To evaluate a logical identity
Searching of an algebraic expression
There are _________ numbers of Boolean functions of degree n.
n
2 ∧ (2*n)
n ∧ 3
n ∧ (n*2)
Inversion of single bit input to a single bit output using _________
NOT gate
NOR gate
AND gate
NAND gate
Which of the following is/are the universal logic gates?
OR and NOR
AND
NAND and NOR
NOT
Which of the following is a Simplification law?
M.(~M+N) = M.N
M+(N.O) = (M+N)(M+O)
~(M+N) = ~M.~N
M.(N.O) = (M.N).O
What is the definition of Boolean functions?
An arithmetic function with k degrees such that f:Y–>Y^k
A special mathematical function with n degrees such that f:Y^n–>Y
An algebraic function with n degrees such that f:X^n–>X
A polynomial function with k degrees such that f:X^2–>X^n
a ⊕ b = ________
(a+b)(a`+b`)
(a+b`)
b`
a` + b`
The set for which the Boolean function is functionally complete is __________
{*, %, /}
{., +, -}
{^, +, -}
{%, +, *}
X+Y`)(X+Z) can be represented by _____
(X+Y`Z)
(Y+X`)
XY`
(X+Z`)
Every poset that is a complete semilattice must always be a _______
sublattice
complete lattice
free lattice
partial lattice
A free semilattice has the _______ property.
intersection
commutative and associative
identity
universal
What rules of inference are used in this argument?
“Jay is an awesome student. Jay is also a good dancer. Therefore, Jay is an awesome student and a good dancer.”
Conjunction
Modus ponens
Disjunctive syllogism
Simplification
The statement, “At least one of your friends is perfect”. Let P (x) be “x is perfect” and let F (x) be “x is your friend” and let the domain be all people.
∀x (F (x) → P (x))
∀x (F (x) ∧ P (x))
∃x (F (x) ∧ P (x))
∃x (F (x) → P (x))
”Everyone wants to learn cosmology.” This argument may be true for which domains?
All students in your cosmology class
All the cosmology learning students in the world
Both of the mentioned
None of the mentioned
